Thickness measurements of ancient prehistoric native american pot shards discovered in a hopi village are approximately normally distributed, with a mean of 4.5 millimeters (mm) and a standard deviation of 1.5 mm. for a randomly found shard, find the following probabilities. (round your answers to four decimal ) the thickness is less than 3.0 mm(b) the thickness is more than 7.0 mm(c) the thickness is between 3.0 mm and 7.0 mm

a) 0.1587

b) 0.0475

c) 0.7938

Step-by-step explanation:

Let's start defining our random variable.

X : ''Thickness (in mm) of ancient prehistoric Native American pot shards discovered in a Hopi village''

X is modeled as a normal random variable.

X ~ N(μ,σ)

Where μ is the mean and σ is the standard deviation.

To calculate all the probabilities, we are going to normalize the random variable X.

We are going to call to the standard normal distribution ''Z''.

[(X - μ) / σ] ≅ Z

We normalize by subtracting the mean to X and then dividing by standard deviation.

We can find the values of probabilities for Z in a standard normal distribution table.

We are going to call Φ(A) to the normal standard cumulative distribution evaluated in a value ''A''

a)

Φ(-1) = 0.1587

b)

1 - Φ(1.666) = 1 - 0.9525 = 0.0475

c)

Φ(1.666) - Φ(-1) = 0.9525 - 0.1587 = 0.7938

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.